{"id":"W2154942876","doi":"10.1109/sfcs.1991.185387","title":"Size-depth tradeoffs for algebraic formulae","year":2002,"lang":"en","type":"article","venue":"","topic":"Algorithms and Data Compression","field":"Computer Science","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Algebraic number; Omega; Mathematics; Upper and lower bounds; Combinatorics; Discrete mathematics; Physics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0000855428,0.00009884855,0.0001057799,0.00003083433,0.0001259812,0.0001205404,0.0006835033,0.00004365155,0.0002256291],"category_scores_gemma":[0.00003176744,0.00007370454,0.00006858104,0.0001354563,0.00001317275,0.0006333623,0.0001579098,0.00005085517,0.0001328302],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001190172,"about_ca_system_score_gemma":0.000007074419,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009500346,"about_ca_topic_score_gemma":0.00000473998,"domain_scores_codex":[0.9991501,0.00001008242,0.0001421533,0.0002876555,0.0001546526,0.0002553587],"domain_scores_gemma":[0.9992085,0.0001621207,0.00003441193,0.0004779178,0.00002771824,0.00008937002],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000003468688,0.0001450157,0.0000486218,0.00001547137,0.0000128587,0.000005471891,0.0003242581,0.0000122549,0.000623945,0.1780201,0.1937968,0.6269917],"study_design_scores_gemma":[0.0007206509,0.0001479951,0.0006788391,0.000009717648,0.000003658583,0.00001546882,0.00001040893,0.7492694,0.002355908,0.01363534,0.2329124,0.0002402355],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0006608029,0.0001515399,0.9851577,0.001385874,0.0002709486,0.0001927582,0.00000478096,0.0002667521,0.01190885],"genre_scores_gemma":[0.3921176,0.00003218115,0.5970088,0.001746311,0.0002116883,0.00004844461,0.000005221115,0.00001606978,0.0088137],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.7492571,"threshold_uncertainty_score":0.3005584,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03212410337113941,"score_gpt":0.2412865495128087,"score_spread":0.2091624461416693,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}